Existence and localization results are derived from Krasnoselskii’s compressionexpansion fixed point theorem in cones, for operator equations in spaces of continuous functions from a compact real interval to an abstract space. The main idea, first used in , is to handle two equivalent operator forms of the equation, one of fixed point type giving the operator to which Krasnoselskii’s theorem applies and an other one of coincidence type which is used to localize a positive solution in a shell. An application is presented for a boundary value problem associated to a fourth order partial differential equation on a rectangular domain.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Positive solution; Boundary value problem; Fixed point theorem in cones.
R. Precup, Positive solutions of evolution operator equations, Austral. J. Math. Anal. Appl. 2 (2005) no. 1, 1-10.
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Australian Journal of Mathematical Anaysis and Applications
MR2133376, Zbl 1078.47059,
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